Abstract
In this chapter, we present our novel geometric data structure, the Inner Sphere Trees. It is the first data structure that is able to compute the penetration volume between a pair of colliding objects at haptic rates. This new contact information guarantees physically-plausible and continuous forces and torques for a stable collision response that is essential for stable haptic rendering. Moreover, we propose a new clustering-based algorithm for creating bounding volume hierarchies and a time-critical traversal scheme for time-budgeted collision detection scenarios.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
However, also this is not really necessary. In the future, we plan to move also the smallest enclosing sphere computation to the GPU. Then we only have to read back the whole hierarchy once.
- 2.
Please visit http://cgvr.informatik.uni-bremen.de/research/ist to watch some videos of our benchmarks.
References
Agarwal, P., Guibas, L., Nguyen, A., Russel, D., & Zhang, L. (2004). Collision detection for deforming necklaces. Computational Geometry, 28, 137–163.
Bradshaw, G., & O’Sullivan, C. (2004). Adaptive medial-axis approximation for sphere-tree construction. ACM Transactions on Graphics, 23(1), 1–26. doi:10.1145/966131.966132. URL http://doi.acm.org/10.1145/966131.966132.
Cottrell, M., Hammer, B., Hasenfuss, A., & Villmann, T. (2006). Batch and median neural gas. Neural Networks, 19, 762–771.
Fisher, S., & Lin, M. (2001). Fast penetration depth estimation for elastic bodies using deformed distance fields. In Proc. international conf. on intelligent robots and systems (IROS) (pp. 330–336).
Gärtner, B. (1999). Fast and robust smallest enclosing balls. In J. Nesetril (Ed.), Lecture notes in computer science: Vol. 1643. ESA (pp. 325–338). Berlin: Springer. ISBN 3-540-66251-0. URL http://link.springer.de/link/service/series/0558/bibs/1643/16430325.htm.
Hammer, B., Hasenfuss, A., & Villmann, T. (2006). Magnification control for batch neural gas. In ESANN (pp. 7–12). URL http://www.dice.ucl.ac.be/Proceedings/esann/esannpdf/es2006-83.pdf.
Hubbard, P. M. (1995). Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 1(3), 218–230.
Liu, F., Harada, T., Lee, Y., & Kim, Y. J. (2010). Real-time collision culling of a million bodies on graphics processing units. ACM Transactions on Graphics, 29(6), 154:1–154:8. doi:10.1145/1882261.1866180. URL http://doi.acm.org/10.1145/1882261.1866180.
Mainzer, D., Weller, R., & Zachmann, G. (2011). Kollisionserkennung und natürliche interaktion in virtuellen umgebungen. In W. Schreiber & P. Zimmermann (Eds.), Virtuelle Techniken im industriellen Umfeld (pp. 33–38, 114–116). Berlin: Springer. Chaps. 3.2, 3.4. ISBN 978-3-642-20635-1. URL http://www.springer.com/engineering/signals/book/978-3-642-20635-1.
Martinetz, T. M., Berkovich, S. G., & Schulten, K. J. (1993). ‘Neural-gas’ network for vector quantization and its application to time-series prediction. IEEE Transactions on Neural Networks, 4(4), 558–569.
O’Brien, J. F., & Hodgins, J. K. (1999). Graphical modeling and animation of brittle fracture. In Proceedings of the 26th annual conference on computer graphics and interactive techniques, SIGGRAPH ’99 (pp. 137–146). New York: ACM Press/Addison-Wesley Publishing Co. ISBN 0-201-48560-5. doi:10.1145/311535.311550.
Satish, N., Harris, M., & Garland, M. (2009). Designing efficient sorting algorithms for manycore GPUs. In Proceedings of the 23rd IEEE international parallel and distributed processing symposium, May.
Schneider, P. J., & Eberly, D. (2002). Geometric tools for computer graphics. New York: Elsevier Science Inc. ISBN 1558605940.
Sengupta, S., Harris, M., & Garland, M. (2008). Efficient parallel scan algorithms for GPUs (Technical Report NVR-2008-003). NVIDIA Corporation. December. URL http://mgarland.org/papers.html#segscan-tr.
Weisstein, E. W. (2012). Sphere-sphere intersection. URL http://mathworld.wolfram.com/Sphere-SphereIntersection.html.
Weisstein, E. W. (2012). Spherical cap. URL http://mathworld.wolfram.com/SphericalCap.html.
Weller, R., & Zachmann, G. (2008). Inner sphere trees (Technical Report IfI-08-09). Department of Informatics, Clausthal University of Technology, October.
Weller, R., & Zachmann, G. (2009). Inner sphere trees for proximity and penetration queries. In 2009 robotics: science and systems conference (RSS), Seattle, WA, USA, June. URL http://cg.in.tu-clausthal.de/research/ist.
Weller, R., & Zachmann, G. (2009). A unified approach for physically-based simulations and haptic rendering. In Sandbox 2009: ACM SIGGRAPH video game proceedings, New Orleans, LA, USA, August. New York: ACM Press. URL http://cg.in.tu-clausthal.de/research/ist.
Weller, R., & Zachmann, G. (2011). Inner sphere trees and their application to collision detection. In S. Coquillart, G. Brunnett, & G. Welch (Eds.), Virtual realities (pp. 181–202). Berlin: Springer (Dagstuhl). Chap. 10. ISBN 978-3-211-99177-0. doi:10.1007/978-3-211-99178-7.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Weller, R. (2013). Inner Sphere Trees. In: New Geometric Data Structures for Collision Detection and Haptics. Springer Series on Touch and Haptic Systems. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-01020-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-01020-5_5
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-01019-9
Online ISBN: 978-3-319-01020-5
eBook Packages: Computer ScienceComputer Science (R0)